This invention relates to optical metrology of materials. More specifically, it provides a novel method for inferring optical properties in spectral ranges that may not be readily accessible experimentally.
Thin-film fabrication and characterization have become an indispensable part of modern technology. Practical applications increasingly demand that the characterization of the fabricated films be carried out in a convenient, accurate, real-time, and customized fashion.
Among the physical characteristics that are of practical importance are the optical properties of materials. Such properties are not only of fundamental and practical significance in their own rights, they are also intimately related to other physical characteristics, such as electrical properties. A method that has proved to be particularly effective in characterizing the optical properties of thin films is the so-called xe2x80x9cnandkxe2x80x9d method. This is a measurement technique that simultaneously determines the thickness d, spectra of physical constantsxe2x80x94namely, index of refraction n and extinction coefficient k, energy band-gap Eg, and interface roughness "sgr" of thin films deposited on opague or transparent substrates. At the core of the xe2x80x9cnandkxe2x80x9d method are the original Forouhi-Bloomer dispersion equations for n and k, as described in U.S. Pat. No. 4,905,170. It is applicable to a broad range of semiconductor, dielectric and thin metal films, and is valid from the vacuum-ultra-violet (VUV) to the near-infra-red (NIR) range in spectrum. The xe2x80x9cnandkxe2x80x9d method has been widely used in the spectrum range extending from 190 to 1000 nm, yielding a great deal of information about the optical and dielectric properties of various think-film materials.
The optical properties in the spectrum ranges below 190 nm and above 1000 nm are also of considerable interest. However, the body of the data in these spectral ranges is strikingly sparse, relative to what is available in the DUV, visible and NIR ranges. This is largely due to the fact that the measurement instrument in these xe2x80x9cextremexe2x80x9d spectral ranges is yet to be readily available, owing to various experimental limitations. Therefore, it would be very useful to extend the xe2x80x9cnandkxe2x80x9d method to these extreme spectral ranges, without the need of carrying out the actual measurements.
Accordingly it is a principal object of the present invention to provide a method for inferring optical parameters of a sample in a predictive spectral range that may not be readily accessible experimentally. The method of the present invention utilizes the measurements of the optical parameters in a predetermined spectral range where the optical parameters can be determined with sufficient details, to extract the information about the parameters in the predictive spectral range.
These and other objects and advantages will become apparent from the following description and accompanying drawings.
The present invention provides a method for inferring optical parameters of a sample in a predictive spectral range by using the known values of the optical parameters in a predetermined measurement spectral range. The method of the present invention capitalizes on the Forouhi-Bloomer dispersion equations for the optical constants n and k.
More specifically, the inventive method utilizes the xe2x80x9cnandkxe2x80x9d method to obtain the xe2x80x9cmeasuredxe2x80x9d values of n and k as functions of wavelength xcex respectively in a predetermined measurement spectral range. The measurements are carried out at a resolution of xcex that is sufficing to bring out the details of n and k spectra. It then constructs the analytical expressions for n=n(E) and k=k(E) in a predictive spectral range by use of the Forouhi-Bloomer dispersion equations for n and k, until the xe2x80x9cinferredxe2x80x9d values of n and k given by the constructed analytical expressions agree with the xe2x80x9cmeasuredxe2x80x9d values obtained from the experimental measurements. The thus constructed analytical expressions n=n(E) and k=k(E) can be subsequently used to provide the optical constants in the predictive spectral range.
The method of the present invention can be applied to a variety of applications in which it is desirable to obtain the optical properties of a sample in a particular spectral range that may not be readily accessible experimentally. It can also be utilized in situations where a quick and reliable estimation of various optical properties is needed, before carrying out laborious experimentation.
As a way of demonstrating the utility of the present invention, the inventive method can be used to deduce the dielectric constant xcexa of a material, thereby averting experimental measurements of capacitance (or other physical parameters) that have been conventionally used to determine xcexa.
The novel features of this invention, as well as the invention itself, will be best understood from the following drawings and detailed description.